Top-k from a Stream with a Heap

You're reading millions of scored items, such as search results or log events, and need the k largest. Sorting everything is $O(n \log n)$ and needs all the data in memory. A size-k min-heap does it in $O(n \log k)$ in one pass.

Implement top_k(stream, k, key=lambda x: x):

• stream is any iterable (possibly a generator you can only read once).
• Return the k items with the largest key, sorted from largest to smallest. If several items tie, the one that appeared earlier comes first.
• Return all items, sorted, if there are fewer than k. Return [] for k <= 0.

Don't sort the whole stream or call heapq.nlargest. Write the heap logic yourself with heapq.heappush and heapq.heappushpop.